Abstract

A calculation method for a quadrature phase-shifting interferometer is presented, and its applications to specular and speckle interferometers and digital holography are described. Two sets of quadrature phase-shifted interferograms are acquired, and the calculation method proposed gives the phase distribution of the interferograms. The principle of the calculation method with error analysis and experimental results for specular and speckle interferometers and digital holography are also given.

© 2012 Optical Society of America

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    [CrossRef]
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  26. K. Tsukamoto, C. Li, H. Kobayashi, and T. Maki, “In situ observation of crystal growth processes under microgravity, using aircraft and drop facility,” J. Jpn. Soc. Microgravity Appl. 18, 190–196 (2001).
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    [CrossRef]
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    [CrossRef]
  29. Y. Awatsuji, M. Sasada, and T. Kubota, “Parallel quasi-phase-shifting digital holography,” Appl. Phys. Lett. 85, 1069–1071 (2004).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  33. D.-I. Serrano-García, N.-I. Toto-Arellano, A. Martínez-García, J.-A. Rayas-Álvarez, G. Rodriguez-Zurita, and A. Montes-Pérez, “Adjustable-window grating interferometer based on a Mach–Zehnder configuration for phase profile measurement of transparent samples,” Opt. Eng. 51, 055601 (2012).
    [CrossRef]
  34. D. G. Abdelsalam, B. Yao, P. Gao, J. Min, and R. Guo, “Single-shot parallel four-step phase shifting using on-axis Fizeau interferometry,” Appl. Opt. 51, 4891–4895 (2012).
    [CrossRef]
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  36. J. Vargas, J. A. Quiroga, C. O. S. Sorzano, J. C. Estrada, and J. M. Carazo, “Two-step demodulation based on the Gram–Schmidt orthonormalization method,” Opt. Lett. 37, 443–445 (2012).
    [CrossRef]

2012

D.-I. Serrano-García, N.-I. Toto-Arellano, A. Martínez-García, and G. Rodriguez-Zurita, “Radial slope measurement of dynamic transparent samples,” J. Opt. 14, 045706 (2012).
[CrossRef]

D.-I. Serrano-García, N.-I. Toto-Arellano, A. Martínez-García, J.-A. Rayas-Álvarez, G. Rodriguez-Zurita, and A. Montes-Pérez, “Adjustable-window grating interferometer based on a Mach–Zehnder configuration for phase profile measurement of transparent samples,” Opt. Eng. 51, 055601 (2012).
[CrossRef]

J. Vargas, J. A. Quiroga, C. O. S. Sorzano, J. C. Estrada, and J. M. Carazo, “Two-step demodulation based on the Gram–Schmidt orthonormalization method,” Opt. Lett. 37, 443–445 (2012).
[CrossRef]

D. G. Abdelsalam, B. Yao, P. Gao, J. Min, and R. Guo, “Single-shot parallel four-step phase shifting using on-axis Fizeau interferometry,” Appl. Opt. 51, 4891–4895 (2012).
[CrossRef]

2011

2010

T. Kiire, T. Yatagai, S. Nakadate, and M. Shibuya, “Quadrature phase-shifting interferometer with a polarization imaging camera,” Opt. Rev. 17, 210–213 (2010).
[CrossRef]

2009

2008

2006

2005

M. N. Morris, J. Millerd, N. Brock, J. Hayes, and B. Saif, “Dynamic phase-shifting electronic speckle pattern interferometer,” Proc. SPIE 5869, 58691B (2005).

2004

J. Millerd, N. Brock, J. Hayes, M. North-Morris, M. Novak, and J. C. Wyant, “Pixelated phase-mask dynamic interferometer,” Proc. SPIE 5531, 304–314 (2004).
[CrossRef]

Y. Awatsuji, M. Sasada, and T. Kubota, “Parallel quasi-phase-shifting digital holography,” Appl. Phys. Lett. 85, 1069–1071 (2004).
[CrossRef]

S. Nakadate, T. Kiire, K. Shiozawa, and M. Shibuya, “Phase-shifting interferometer using two phase-shifted fringe patterns in quadrature,” Jpn. J. Opt. 33, 407–412 (2004).

2001

K. Tsukamoto, C. Li, H. Kobayashi, and T. Maki, “In situ observation of crystal growth processes under microgravity, using aircraft and drop facility,” J. Jpn. Soc. Microgravity Appl. 18, 190–196 (2001).

1999

S. Maruyama, T. Shibata, and K. Tsukamoto, “Measurement of diffusion fields of solutions using real-time phase-shift interferometer and rapid heat-transfer control system,” Exp. Therm. Fluid Sci. 19, 34–48 (1999).
[CrossRef]

1997

1995

S. Nakadate and M. Isshiki, “Real-time fringe pattern processing and its applications,” Proc. SPIE 2544, 74–86 (1995).
[CrossRef]

T.-C. Poon, K. Doh, B. Schilling, M. Wu, K. Shinoda, and Y. Suzuki, “Three-dimensional microscopy by optical scanning holography,” Opt. Eng. 34, 1338–1344 (1995).
[CrossRef]

1994

1993

K. Onuma, K. Tsukamoto, and S. Nakadate, “Application of real time phase shift interferometer to the measurement of concentration field,” J. Cryst. Growth 129, 706–718 (1993).
[CrossRef]

C. L. Koliopoulos and M. Jensen, “Real-time video rate phase processor,” Proc. SPIE 2003, 264–268 (1993).
[CrossRef]

1992

1991

C. L. Koliopoulos, “Simultaneous phase shift interferometer,” Proc. SPIE 1531, 119–127 (1991).
[CrossRef]

1989

J. Roehrig, P. Ehrensberger, and M. Okamura, “High speed, large format wavefront sensor employing hexflash phase analysis,” Proc. SPIE 1163, 44–50 (1989).
[CrossRef]

1987

L. Onural and P. D. Scott, “Digital decoding of in-line holograms,” Opt. Eng. 26, 261124 (1987).
[CrossRef]

O. Y. Kwon, D. M. Shough, and R. A. Williams, “Stroboscopic phase-shifting interferometry,” Opt. Lett. 12, 855–857 (1987).
[CrossRef]

1985

1984

R. Smythe and R. Moore, “Instantaneous phase measuring interferometry,” Opt. Eng. 23, 234361 (1984).
[CrossRef]

O. Y. Kwon, “Multichannel phase-shifted interferometer,” Opt. Lett. 9, 59–61 (1984).
[CrossRef]

1983

1972

M. Kronrod, N. Merzlyakov, and L. Yaroslavskii, “Reconstruction of a hologram with computer,” Sov. Phys. Tech. Phys. 17, 333–334 (1972).

Abdelsalam, D. G.

Awatsuji, Y.

Y. Awatsuji, T. Tahara, A. Kaneko, T. Koyama, K. Nishio, S. Ura, T. Kubota, and O. Matoba, “Parallel two-step phase-shifting digital holography,” Appl. Opt. 47, D183–D189(2008).
[CrossRef]

Y. Awatsuji, M. Sasada, and T. Kubota, “Parallel quasi-phase-shifting digital holography,” Appl. Phys. Lett. 85, 1069–1071 (2004).
[CrossRef]

Bareket, N.

N. Bareket, “Three-channel phase detector for pulsed wavefront sensing,” Proc. SPIE 551, 12–16 (1985).
[CrossRef]

Brock, N.

M. N. Morris, J. Millerd, N. Brock, J. Hayes, and B. Saif, “Dynamic phase-shifting electronic speckle pattern interferometer,” Proc. SPIE 5869, 58691B (2005).

J. Millerd, N. Brock, J. Hayes, M. North-Morris, M. Novak, and J. C. Wyant, “Pixelated phase-mask dynamic interferometer,” Proc. SPIE 5531, 304–314 (2004).
[CrossRef]

Carazo, J. M.

Colucci, D.

Creath, K.

Doh, K.

T.-C. Poon, K. Doh, B. Schilling, M. Wu, K. Shinoda, and Y. Suzuki, “Three-dimensional microscopy by optical scanning holography,” Opt. Eng. 34, 1338–1344 (1995).
[CrossRef]

Ehrensberger, P.

J. Roehrig, P. Ehrensberger, and M. Okamura, “High speed, large format wavefront sensor employing hexflash phase analysis,” Proc. SPIE 1163, 44–50 (1989).
[CrossRef]

Estrada, J. C.

Gao, P.

Guo, R.

Hayes, J.

M. N. Morris, J. Millerd, N. Brock, J. Hayes, and B. Saif, “Dynamic phase-shifting electronic speckle pattern interferometer,” Proc. SPIE 5869, 58691B (2005).

J. Millerd, N. Brock, J. Hayes, M. North-Morris, M. Novak, and J. C. Wyant, “Pixelated phase-mask dynamic interferometer,” Proc. SPIE 5531, 304–314 (2004).
[CrossRef]

Ida, T.

Isshiki, M.

S. Nakadate and M. Isshiki, “Real-time fringe pattern processing and its applications,” Proc. SPIE 2544, 74–86 (1995).
[CrossRef]

Jensen, M.

C. L. Koliopoulos and M. Jensen, “Real-time video rate phase processor,” Proc. SPIE 2003, 264–268 (1993).
[CrossRef]

Kaneko, A.

Kiire, T.

T. Kiire, T. Yatagai, S. Nakadate, and M. Shibuya, “Quadrature phase-shifting interferometer with a polarization imaging camera,” Opt. Rev. 17, 210–213 (2010).
[CrossRef]

T. Kiire, S. Nakadate, and M. Shibuya, “Digital holography with a quadrature phase-shifting interferometer,” Appl. Opt. 48, 1308–1315 (2009).
[CrossRef]

T. Kiire, S. Nakadate, and M. Shibuya, “Simultaneous formation of four fringes by using a polarization quadrature phase-shifting interferometer with wave plates and a diffraction grating,” Appl. Opt. 47, 4787–4792 (2008).
[CrossRef]

S. Nakadate, T. Kiire, K. Shiozawa, and M. Shibuya, “Phase-shifting interferometer using two phase-shifted fringe patterns in quadrature,” Jpn. J. Opt. 33, 407–412 (2004).

Kobayashi, H.

K. Tsukamoto, C. Li, H. Kobayashi, and T. Maki, “In situ observation of crystal growth processes under microgravity, using aircraft and drop facility,” J. Jpn. Soc. Microgravity Appl. 18, 190–196 (2001).

Koliopoulos, C. L.

C. L. Koliopoulos and M. Jensen, “Real-time video rate phase processor,” Proc. SPIE 2003, 264–268 (1993).
[CrossRef]

C. L. Koliopoulos, “Simultaneous phase shift interferometer,” Proc. SPIE 1531, 119–127 (1991).
[CrossRef]

Koyama, T.

Kronrod, M.

M. Kronrod, N. Merzlyakov, and L. Yaroslavskii, “Reconstruction of a hologram with computer,” Sov. Phys. Tech. Phys. 17, 333–334 (1972).

Kubota, T.

Y. Awatsuji, T. Tahara, A. Kaneko, T. Koyama, K. Nishio, S. Ura, T. Kubota, and O. Matoba, “Parallel two-step phase-shifting digital holography,” Appl. Opt. 47, D183–D189(2008).
[CrossRef]

Y. Awatsuji, M. Sasada, and T. Kubota, “Parallel quasi-phase-shifting digital holography,” Appl. Phys. Lett. 85, 1069–1071 (2004).
[CrossRef]

Kwon, O. Y.

Li, C.

K. Tsukamoto, C. Li, H. Kobayashi, and T. Maki, “In situ observation of crystal growth processes under microgravity, using aircraft and drop facility,” J. Jpn. Soc. Microgravity Appl. 18, 190–196 (2001).

Maki, T.

K. Tsukamoto, C. Li, H. Kobayashi, and T. Maki, “In situ observation of crystal growth processes under microgravity, using aircraft and drop facility,” J. Jpn. Soc. Microgravity Appl. 18, 190–196 (2001).

Martínez-García, A.

D.-I. Serrano-García, N.-I. Toto-Arellano, A. Martínez-García, and G. Rodriguez-Zurita, “Radial slope measurement of dynamic transparent samples,” J. Opt. 14, 045706 (2012).
[CrossRef]

D.-I. Serrano-García, N.-I. Toto-Arellano, A. Martínez-García, J.-A. Rayas-Álvarez, G. Rodriguez-Zurita, and A. Montes-Pérez, “Adjustable-window grating interferometer based on a Mach–Zehnder configuration for phase profile measurement of transparent samples,” Opt. Eng. 51, 055601 (2012).
[CrossRef]

Maruyama, S.

S. Maruyama, T. Shibata, and K. Tsukamoto, “Measurement of diffusion fields of solutions using real-time phase-shift interferometer and rapid heat-transfer control system,” Exp. Therm. Fluid Sci. 19, 34–48 (1999).
[CrossRef]

Matoba, O.

Mertz, L.

Merzlyakov, N.

M. Kronrod, N. Merzlyakov, and L. Yaroslavskii, “Reconstruction of a hologram with computer,” Sov. Phys. Tech. Phys. 17, 333–334 (1972).

Millerd, J.

M. N. Morris, J. Millerd, N. Brock, J. Hayes, and B. Saif, “Dynamic phase-shifting electronic speckle pattern interferometer,” Proc. SPIE 5869, 58691B (2005).

J. Millerd, N. Brock, J. Hayes, M. North-Morris, M. Novak, and J. C. Wyant, “Pixelated phase-mask dynamic interferometer,” Proc. SPIE 5531, 304–314 (2004).
[CrossRef]

Min, J.

Montes-Pérez, A.

D.-I. Serrano-García, N.-I. Toto-Arellano, A. Martínez-García, J.-A. Rayas-Álvarez, G. Rodriguez-Zurita, and A. Montes-Pérez, “Adjustable-window grating interferometer based on a Mach–Zehnder configuration for phase profile measurement of transparent samples,” Opt. Eng. 51, 055601 (2012).
[CrossRef]

Moore, R.

R. Smythe and R. Moore, “Instantaneous phase measuring interferometry,” Opt. Eng. 23, 234361 (1984).
[CrossRef]

Morris, M. N.

M. N. Morris, J. Millerd, N. Brock, J. Hayes, and B. Saif, “Dynamic phase-shifting electronic speckle pattern interferometer,” Proc. SPIE 5869, 58691B (2005).

Murata, S.

Nakadate, S.

T. Kiire, T. Yatagai, S. Nakadate, and M. Shibuya, “Quadrature phase-shifting interferometer with a polarization imaging camera,” Opt. Rev. 17, 210–213 (2010).
[CrossRef]

T. Kiire, S. Nakadate, and M. Shibuya, “Digital holography with a quadrature phase-shifting interferometer,” Appl. Opt. 48, 1308–1315 (2009).
[CrossRef]

T. Kiire, S. Nakadate, and M. Shibuya, “Simultaneous formation of four fringes by using a polarization quadrature phase-shifting interferometer with wave plates and a diffraction grating,” Appl. Opt. 47, 4787–4792 (2008).
[CrossRef]

S. Nakadate, T. Kiire, K. Shiozawa, and M. Shibuya, “Phase-shifting interferometer using two phase-shifted fringe patterns in quadrature,” Jpn. J. Opt. 33, 407–412 (2004).

S. Nakadate and M. Isshiki, “Real-time fringe pattern processing and its applications,” Proc. SPIE 2544, 74–86 (1995).
[CrossRef]

K. Onuma, K. Tsukamoto, and S. Nakadate, “Application of real time phase shift interferometer to the measurement of concentration field,” J. Cryst. Growth 129, 706–718 (1993).
[CrossRef]

S. Nakadate and H. Saito, “Fringe scanning speckle-pattern interferometry,” Appl. Opt. 24, 2172–2180 (1985).
[CrossRef]

Nishio, K.

Nitanai, E.

Nomura, T.

North-Morris, M.

J. Millerd, N. Brock, J. Hayes, M. North-Morris, M. Novak, and J. C. Wyant, “Pixelated phase-mask dynamic interferometer,” Proc. SPIE 5531, 304–314 (2004).
[CrossRef]

Novak, M.

J. Millerd, N. Brock, J. Hayes, M. North-Morris, M. Novak, and J. C. Wyant, “Pixelated phase-mask dynamic interferometer,” Proc. SPIE 5531, 304–314 (2004).
[CrossRef]

Numata, T.

Okamura, M.

J. Roehrig, P. Ehrensberger, and M. Okamura, “High speed, large format wavefront sensor employing hexflash phase analysis,” Proc. SPIE 1163, 44–50 (1989).
[CrossRef]

Onuma, K.

K. Onuma, K. Tsukamoto, and S. Nakadate, “Application of real time phase shift interferometer to the measurement of concentration field,” J. Cryst. Growth 129, 706–718 (1993).
[CrossRef]

Onural, L.

L. Onural and P. D. Scott, “Digital decoding of in-line holograms,” Opt. Eng. 26, 261124 (1987).
[CrossRef]

Poon, T.-C.

T.-C. Poon, K. Doh, B. Schilling, M. Wu, K. Shinoda, and Y. Suzuki, “Three-dimensional microscopy by optical scanning holography,” Opt. Eng. 34, 1338–1344 (1995).
[CrossRef]

Quiroga, J. A.

Rayas-Álvarez, J.-A.

D.-I. Serrano-García, N.-I. Toto-Arellano, A. Martínez-García, J.-A. Rayas-Álvarez, G. Rodriguez-Zurita, and A. Montes-Pérez, “Adjustable-window grating interferometer based on a Mach–Zehnder configuration for phase profile measurement of transparent samples,” Opt. Eng. 51, 055601 (2012).
[CrossRef]

Rodriguez-Zurita, G.

D.-I. Serrano-García, N.-I. Toto-Arellano, A. Martínez-García, J.-A. Rayas-Álvarez, G. Rodriguez-Zurita, and A. Montes-Pérez, “Adjustable-window grating interferometer based on a Mach–Zehnder configuration for phase profile measurement of transparent samples,” Opt. Eng. 51, 055601 (2012).
[CrossRef]

D.-I. Serrano-García, N.-I. Toto-Arellano, A. Martínez-García, and G. Rodriguez-Zurita, “Radial slope measurement of dynamic transparent samples,” J. Opt. 14, 045706 (2012).
[CrossRef]

Roehrig, J.

J. Roehrig, P. Ehrensberger, and M. Okamura, “High speed, large format wavefront sensor employing hexflash phase analysis,” Proc. SPIE 1163, 44–50 (1989).
[CrossRef]

Saif, B.

M. N. Morris, J. Millerd, N. Brock, J. Hayes, and B. Saif, “Dynamic phase-shifting electronic speckle pattern interferometer,” Proc. SPIE 5869, 58691B (2005).

Saito, H.

Sasada, M.

Y. Awatsuji, M. Sasada, and T. Kubota, “Parallel quasi-phase-shifting digital holography,” Appl. Phys. Lett. 85, 1069–1071 (2004).
[CrossRef]

Schilling, B.

T.-C. Poon, K. Doh, B. Schilling, M. Wu, K. Shinoda, and Y. Suzuki, “Three-dimensional microscopy by optical scanning holography,” Opt. Eng. 34, 1338–1344 (1995).
[CrossRef]

Schnars, U.

Scott, P. D.

L. Onural and P. D. Scott, “Digital decoding of in-line holograms,” Opt. Eng. 26, 261124 (1987).
[CrossRef]

Serrano-García, D.-I.

D.-I. Serrano-García, N.-I. Toto-Arellano, A. Martínez-García, and G. Rodriguez-Zurita, “Radial slope measurement of dynamic transparent samples,” J. Opt. 14, 045706 (2012).
[CrossRef]

D.-I. Serrano-García, N.-I. Toto-Arellano, A. Martínez-García, J.-A. Rayas-Álvarez, G. Rodriguez-Zurita, and A. Montes-Pérez, “Adjustable-window grating interferometer based on a Mach–Zehnder configuration for phase profile measurement of transparent samples,” Opt. Eng. 51, 055601 (2012).
[CrossRef]

Shibata, T.

S. Maruyama, T. Shibata, and K. Tsukamoto, “Measurement of diffusion fields of solutions using real-time phase-shift interferometer and rapid heat-transfer control system,” Exp. Therm. Fluid Sci. 19, 34–48 (1999).
[CrossRef]

Shibuya, M.

T. Kiire, T. Yatagai, S. Nakadate, and M. Shibuya, “Quadrature phase-shifting interferometer with a polarization imaging camera,” Opt. Rev. 17, 210–213 (2010).
[CrossRef]

T. Kiire, S. Nakadate, and M. Shibuya, “Digital holography with a quadrature phase-shifting interferometer,” Appl. Opt. 48, 1308–1315 (2009).
[CrossRef]

T. Kiire, S. Nakadate, and M. Shibuya, “Simultaneous formation of four fringes by using a polarization quadrature phase-shifting interferometer with wave plates and a diffraction grating,” Appl. Opt. 47, 4787–4792 (2008).
[CrossRef]

S. Nakadate, T. Kiire, K. Shiozawa, and M. Shibuya, “Phase-shifting interferometer using two phase-shifted fringe patterns in quadrature,” Jpn. J. Opt. 33, 407–412 (2004).

Shinoda, K.

T.-C. Poon, K. Doh, B. Schilling, M. Wu, K. Shinoda, and Y. Suzuki, “Three-dimensional microscopy by optical scanning holography,” Opt. Eng. 34, 1338–1344 (1995).
[CrossRef]

Shiozawa, K.

S. Nakadate, T. Kiire, K. Shiozawa, and M. Shibuya, “Phase-shifting interferometer using two phase-shifted fringe patterns in quadrature,” Jpn. J. Opt. 33, 407–412 (2004).

Shough, D. M.

Smythe, R.

R. Smythe and R. Moore, “Instantaneous phase measuring interferometry,” Opt. Eng. 23, 234361 (1984).
[CrossRef]

Sorzano, C. O. S.

Suzuki, Y.

T.-C. Poon, K. Doh, B. Schilling, M. Wu, K. Shinoda, and Y. Suzuki, “Three-dimensional microscopy by optical scanning holography,” Opt. Eng. 34, 1338–1344 (1995).
[CrossRef]

Tahara, T.

Toto-Arellano, N.-I.

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[CrossRef]

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J. Millerd, N. Brock, J. Hayes, M. North-Morris, M. Novak, and J. C. Wyant, “Pixelated phase-mask dynamic interferometer,” Proc. SPIE 5531, 304–314 (2004).
[CrossRef]

Yamaguchi, I.

Yamashita, K.

Yao, B.

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M. Kronrod, N. Merzlyakov, and L. Yaroslavskii, “Reconstruction of a hologram with computer,” Sov. Phys. Tech. Phys. 17, 333–334 (1972).

Yatagai, T.

T. Kiire, T. Yatagai, S. Nakadate, and M. Shibuya, “Quadrature phase-shifting interferometer with a polarization imaging camera,” Opt. Rev. 17, 210–213 (2010).
[CrossRef]

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[CrossRef]

T. Kiire, S. Nakadate, and M. Shibuya, “Simultaneous formation of four fringes by using a polarization quadrature phase-shifting interferometer with wave plates and a diffraction grating,” Appl. Opt. 47, 4787–4792 (2008).
[CrossRef]

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[CrossRef]

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[CrossRef]

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[CrossRef]

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[CrossRef]

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[CrossRef]

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Y. Awatsuji, M. Sasada, and T. Kubota, “Parallel quasi-phase-shifting digital holography,” Appl. Phys. Lett. 85, 1069–1071 (2004).
[CrossRef]

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S. Maruyama, T. Shibata, and K. Tsukamoto, “Measurement of diffusion fields of solutions using real-time phase-shift interferometer and rapid heat-transfer control system,” Exp. Therm. Fluid Sci. 19, 34–48 (1999).
[CrossRef]

J. Cryst. Growth

K. Onuma, K. Tsukamoto, and S. Nakadate, “Application of real time phase shift interferometer to the measurement of concentration field,” J. Cryst. Growth 129, 706–718 (1993).
[CrossRef]

J. Jpn. Soc. Microgravity Appl.

K. Tsukamoto, C. Li, H. Kobayashi, and T. Maki, “In situ observation of crystal growth processes under microgravity, using aircraft and drop facility,” J. Jpn. Soc. Microgravity Appl. 18, 190–196 (2001).

J. Opt.

D.-I. Serrano-García, N.-I. Toto-Arellano, A. Martínez-García, and G. Rodriguez-Zurita, “Radial slope measurement of dynamic transparent samples,” J. Opt. 14, 045706 (2012).
[CrossRef]

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S. Nakadate, T. Kiire, K. Shiozawa, and M. Shibuya, “Phase-shifting interferometer using two phase-shifted fringe patterns in quadrature,” Jpn. J. Opt. 33, 407–412 (2004).

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[CrossRef]

D.-I. Serrano-García, N.-I. Toto-Arellano, A. Martínez-García, J.-A. Rayas-Álvarez, G. Rodriguez-Zurita, and A. Montes-Pérez, “Adjustable-window grating interferometer based on a Mach–Zehnder configuration for phase profile measurement of transparent samples,” Opt. Eng. 51, 055601 (2012).
[CrossRef]

T.-C. Poon, K. Doh, B. Schilling, M. Wu, K. Shinoda, and Y. Suzuki, “Three-dimensional microscopy by optical scanning holography,” Opt. Eng. 34, 1338–1344 (1995).
[CrossRef]

Opt. Lett.

Opt. Rev.

T. Kiire, T. Yatagai, S. Nakadate, and M. Shibuya, “Quadrature phase-shifting interferometer with a polarization imaging camera,” Opt. Rev. 17, 210–213 (2010).
[CrossRef]

Proc. SPIE

J. Millerd, N. Brock, J. Hayes, M. North-Morris, M. Novak, and J. C. Wyant, “Pixelated phase-mask dynamic interferometer,” Proc. SPIE 5531, 304–314 (2004).
[CrossRef]

M. N. Morris, J. Millerd, N. Brock, J. Hayes, and B. Saif, “Dynamic phase-shifting electronic speckle pattern interferometer,” Proc. SPIE 5869, 58691B (2005).

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Figures (10)

Fig. 1.
Fig. 1.

Fringes in quadrature with tilting 2λ (a), (b) before defocusing of lens and (c), (d) after the defocusing of 2λ during lens testing.

Fig. 2.
Fig. 2.

Resultant phases (a) θ, (b) θ+φ using Eqs. (3) and (4) with Fig. 1, and (c) the phase difference φ between (a) and (b) that corresponds to the defocusing of the lens.

Fig. 3.
Fig. 3.

Sine and cosine coordinates for error analysis: (a) phase error caused by random fluctuations and (b) trajectory of radius vector C2+S2 varying with phase θ.

Fig. 4.
Fig. 4.

Experimental setup of quadrature QPI for a specular object. QWP, quarter wave plate; Pol., polarizer.

Fig. 5.
Fig. 5.

Fringe patterns in quadrature for a stepwise object with specular surface: (a), (b) before bias phase change in the interferometer and (c), (d) after bias phase change of 60.5°.

Fig. 6.
Fig. 6.

Phase images (a) θ and (b) θ+φ calculated with Eqs. (3) and (4), respectively, and (c), (d) obtained by spatial smoothing in 3×3 pixels of (a) and (b), respectively, in which singular points are removed.

Fig. 7.
Fig. 7.

Experimental setup of quadrature phase-shifting speckle interferometer with scattered object and reference. BS, beam splitter; M, mirror; L, lens.

Fig. 8.
Fig. 8.

Experimental results for (a) a scattered circular object. Phase images (b) before displacement and (c) after displacement, obtained by Eqs. (3) and (4), respectively, and (d) phase difference φ between two phases, which is proportional to the longitudinal displacement.

Fig. 9.
Fig. 9.

Experimental setup of quadrature PSDH with scattered surface of a stepwise object. QWP, quarter wave plate; Pol., polarizer.

Fig. 10.
Fig. 10.

(a) Phase distribution calculated by this method and (b), (c) reconstructed images focused on the respective letters “p” and “t” with the phase hologram (a).

Equations (8)

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B2=(I1A)2+(I2A)2=(I3A)2+(I4A)2.
A=I32+I42I12I222(I3+I4I1I2).
θ=tan1((I1I2)2+(I2I3)2+(I2I4)2(I1I2)2(I1I3)2(I1I4)2).
θ+φ=tan1((I1I4)2(I2I4)2+(I3I4)2(I1I3)2+(I2I3)2(I3I4)2).
C=(I1I2)2(I1I3)2(I1I4)2+2σ2,S=(I1I2)2(I2I3)2+(I2I4)22σ2.
Δθ=1|cos(θ+φ2+3π4)||sin(φ2)|·SNR22,
ΔC2+ΔS2=8σ2B2{53cosφ+Rsin(2θ+α)},
Δθ=3·SNR.

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